Bandgap references are widely utilized in integrated circuits to produce a fixed voltage to serve as a reference. The voltage remains constant regardless of power supply variations, temperature changes, and circuit loading from a device. Conventional bandgaps create a current source with the core bipolar devices and cross-couple this source with a current mirror.
Bandgap references are based on temperature behavior of the base-emitter voltage (VBE) of a bipolar junction transistor. When biased in a stable manner, VBE falls with increasing temperature. Thus, VBE is said to have a temperature behavior that is Complimentary to Absolute Temperature (CTAT). Two identical devices having different current densities will have VBE values that fall with temperature at different predictable slopes. These characteristic curves will both converge at zero degrees Kelvin. The difference between the VBE values of the two devices with different current densities (AVBE) increases with temperature. This characteristic is said to be Proportional to Absolute Temperature (PTAT). The appropriate scaling and summation of PTAT and CTAT voltages, produces a voltage that is substantially temperature independent. This serves as the basis for basic bandgap reference techniques.
In most bandgap references, ΔVBE is created by biasing identical devices with different emitter junction areas with either currents of the same magnitude or currents of a stable integer ratio. The created ΔVBE is generally impressed across a resistor to generate a current that is PTAT, which is then scaled by the required factor using a resistor of the same type and added to the VBE to create the reference output voltage. The ΔVBE generator is often referred to as the “bandgap core.” The bandgap core that produces the ΔVBE provides a PTAT current source, such that the core current is PTAT. It is convenient in bandgap implementations, to mirror this core PTAT current from one core bipolar transistor to the other. Mirroring the core PTAT current is performed using a current mirror, a feedback circuit, or both. Since the circuit is stable wherever the current-verses-voltage transfer functions of the current source and mirror cross each other, standard bandgap references have a stable state at zero current which produces zero output voltage.
More specifically, A bipolar junction transistor collector current is given by the following equation:IC=Is*exp(VBE/Vt)  (1)wherein, IC is the collector current, Is is the scale current, VBE is the base-emitter voltage, and Vt is the thermal voltage. Vt is determined by the following equation:Vt=KT/q  (2)wherein, K is Boltzmann's constant, T is the temperature in Kelvin, and q is the electronic charge.
Solving equation (1) for base-emitter voltage yields the following equation:VBE=Vt*ln(IC/Is)  (3)For two devices with different base-emitter voltages, the difference between the VBE values for the two devices, i.e., ΔVBE, is given by the following equation:ΔVBE=(VBE1−VBE2)  (4)Combining equations (3) and (4) provides:ΔVBE=Vt*ln(IC1/Is1)−Vt*ln(IC2/Is2)=Vt*ln [(IC1/IC2)*(Is2/Is1)]  (5)Where IC1 and Is1 are the collector current and scale current for the first device and IC2 and Is2 are the collector current and scale current for the second device.
For identical devices, the scale current is proportional only to the emitter area. Therefore, equation (5) becomes:ΔVBE=Vt*ln [(IC1/IC2)*(AE2/AE1)]  (6)wherein AE1 and AE2 are the emitter areas for the first and second devices, respectively. For practical matching considerations, area ratios are achieved in standard fashion by replication of unit devices. Ratio m results from m devices ratioed with a single device. Thus, equation (6) becomes:ΔVBE=Vt*ln [(IC1/IC2)*(m)]  (7)
In equation (7), only the collector current ratio (IC1/IC2), not its magnitude, is important. For devices driven at the same current, equation (7) becomes:ΔVBE=Vt*ln(m)  (8)Equation (8) is independent of collector current. The ΔVBE expression in equation (8) has all of the VBE-characterizing parameters eliminated, leaving only a simple ratio (m) and the thermal voltage Vt. As provided in Gilbert, “Monolithic Voltage and Current References: Theme and Variations” MEAD Design Course, San Jose, Calif. (1996), equation (8) provides the basis for producing a temperature dependent voltage that is quite fundamental (not empirical). The temperature dependent voltage is proportional to temperature regardless of the absolute value of the operating currents, doping profiles, junction areas, transistor polarity (NPN or PNP), or even the material type (Si, Ge, SIGe, or even Schottky junctions). Only Boltzmann's constant and the charge on an electron and are involved.
Most bandgap references create a current source with the ΔVBE core and cross-couple this source with a current mirror that is balanced either by the mirror itself, or an amplifier servo-loop, or both. This is convenient and reduces curvature slightly, but introduces an undesired zero-current state. Since standard bandgap reference techniques have an undesired zero-current or zero-voltage state, they require a start-up circuit for operation. Although many successful start-up circuits have been developed, they are difficult to design and notoriously difficult to evaluate with complete confidence over all conditions. Start-up circuits also introduce delay in start-up for the bandgap reference circuit.